Syllabus for Quantum Mechanics

Texts:

Introductory Quantum Mechanics, by Richard L. Liboff, (QC 174.12 .L52 2003)
Quantum Chemistry, by Donald A. McQuarrie, (QD 462 .M4 1983)
Lectures on Quantum Mechanics, by Gordon Baym, (QC 174.1.B35)

If you buy only one book for this course, the Liboff text is probably the most useful.

Other Useful Texts:

  • Introduction to Quantum Mechanics in Chemistry, by Mark Ratner and George Schatz, (QD 462.R28 2000)
  • Mathematical Methods in the Physical Sciences, by Mary L. Boas, (QA 37.B662)
  • Quantum Chemistry, by Ira N. Levine (QD 462.L48 1991b)
  • Quantum Mechanics, by Claude Cohen-Tannoudji, Bernard Dui, Frank Laloe, (QC 174.12.C6313)
  • Introduction to Quantum Mechanics, by B.H. Bransden, C.J. Joachain, (QC 174.12 .B74 1989)
  • Quantum Mechanics, by Eugen Merzbacher, (QC 174.1 .M577 1970
  • Quantum Theory, by David Bohm, (QC 174.1.B634)
  • Advanced Quantum Mechanics, by J. J. Sakurai, (QC 174.1.S158 1973)
  • Quantum Mechanics, by L. D. Landau, (QC 174.1.L253)
  • Practical Quantum Mechanics, by Siegfried Flugge, (QC 174.1 .F5713)
  • Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, by Attila Szabo, Neil S. Ostlund, (QD 462.S95 1989)

Course Outline:

  1. Brief Mathematical Review (Liboff: Ch. 1 and Secs. 4.3 & 11.2, also Boas if you can find a copy)
    1. Coordinate systems
    2. Ordinary Differential Equations
    3. Complex numbers, integration, and Cauchy's theorem
    4. Notational conventions - Dirac's Bra-ket notation
    5. Matrices, vectors, eigenvalues, eigenvectors, determinants, and traces
  2. The Schrödinger Equation (McQuarrie: Chapter 3)
    1. Time-dependent
    2. Time-independent
    3. Linear Operators
    4. Particle in a one-dimensional box
  3. Postulates & Theorems (Liboff: Chapters 3 & 4)
    1. The state of the system is given by the wavefunction.
    2. Observables in Classical Mechanics correspond to operators in QM.
    3. QM observables will be measured at the eigenvalues of the operators.
    4. Averages of Quantum observables are obtained from expectation values.
    5. Time-dependence is derived from time-dependent Schrödinger equation.
    6. QM operators are linear Hermitian operators.
    7. Eigenfunctions of Hermitian operators are orthogonal.
    8. Many operators to not commute.
    9. The Schwarz inequality and the uncertainty principle.
  4. The Harmonic Oscillator (Liboff: 7.2, 7.3, Baym: pp. 123-128)
    1. Differential Equations
    2. Raising & Lowering operators
    3. Applications to Spectroscopy
  5. Angular Momentum (Liboff: Sections 9.1, 9.2, 9.3, Baym: Chapter 6)
    1. Seperability
    2. The Laplacian in Spherical Coordinates
    3. The Rigid Rotator
    4. Spherical Harmonics
    5. Commutation of Angular Momentum operators
  6. The Hydrogen Atom (Baym: Chapter 7, Liboff: Sections 10.5, 10.6)
    1. Radial functions
    2. Angular functions
    3. High-Z hydrogenic atoms
  7. Approximate Methods (Baym: Chapter 11, McQuarrie: Sections 7.4-7.7, Liboff: Chapter 13)
    1. Perturbation Theory
      1. Derivation of the Van der Waals Interaction
    2. The Variational Method
  8. Quantum Scattering (Liboff: Sections 7.5, 7.6, 7.7, 7.10)
    1. Transmission through Potential Steps & Barriers
    2. Airy functions & the WKB Approximation
  9. Quantum Statistical Mechanics (Liboff: Chapter 11)
    1. Partition Functions
    2. The Density Matrix